OFFSET
1,2
COMMENTS
See Bacher link for the definition of Euclid-reduced.
LINKS
Roland Bacher, Euclid meets Popeye: The Euclidean Algorithm for 2X2 matrices, arXiv:2209.09529 [math.NT], 2022.
Roland Bacher, Euclid meets Popeye: The Euclidean Algorithm for 2 X 2 Matrices, Comptes rendus de l’Académie des sciences, Volume 361 (2023), p. 889-895.
MathOverflow, Arithmetic properties of positively reduced 2×2-matrices, 2021.
FORMULA
a(n) = Sum_{d|n, d^2>=n} d+1-n/d.
From Ridouane Oudra, Oct 30 2023: (Start)
a(n) = Sum_{d|n} max(d-n/d, 1).
a(n) = ceiling(tau(n)/2) + (1/2)*Sum_{d|n} abs(d-n/d).
G.f.: Sum_{k>=1} x^(k^2) / (1 - x^k)^2. - Ilya Gutkovskiy, May 17 2024
MAPLE
with(numtheory): seq(add(max(d-n/d, 1), d in divisors(n)), n=1..80); # Ridouane Oudra, Oct 30 2023
MATHEMATICA
a[n_] := DivisorSum[n, # + 1 - n/# &, #^2 >= n &]; Array[a, 100] (* Amiram Eldar, Sep 21 2022 *)
PROG
(PARI) a(n) = sumdiv(n, d, if (d^2 >= n, d+1-n/d));
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Sep 21 2022
STATUS
approved